This thread is to document who is fighting who in Game of Thrones (just the TV show things we know, sorry if something is just in the books it shouldn't be here.)

This will be ongoing living document for up through Season Four. Please contribute anything you would like to add or corrections and I will add all contributions to this main post based on all of your responses.

I will save a version of this after each episode, so there will be one of these for each Season 4, episode.
This is to help show the progression.

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In general, at the beginning of Season Four:

Most of the mainland of Westeros is still under control by the Lannisters. Their main enemies are Greyjoys and Baratheons.

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PS1- S4: White Walkers versus Castle Black men;
PS1- S4: White Walkers versus the Wildlings;
PS1- S4: White Walkers versus Westeros;
PS1- S4: Wildlings versus Castle Black men;
PS1- S4: House Baratheon versus House Targaryen; Robert Baratheon killed Rhaegar Targaryen.)
PS1- S4: House Lannister versus House Targaryen; (Jaime killed King Aerys Targaryen.)
S1: House Arryn versus House Lannister; (Sansa Stark may end up with Robin Arryn.)
S1-S4: House Lannister versus House Stark; (Jaime nearly kills Bran; Joffrey had Ned, Catelyn Tully and Robb Stark killed.)
S3-S4: House Bolton versus House Stark; (Robb is killed.)
S3: House Frey versus House Tully; (Catelyn is killed by Walder Frey and Edmure is a captive husband of one of Walder Frey's daughters.)
S3: House Stark versus House Frey; (Catelyn is killed by Walder Frey.)
S4: House Martell versus House Lannister; (Elia Martell was married to a Targaryen killed by the Mountain, sister of Oberyn and now Oberyn is dead.)
S4: The Thenn hate the Hornfoots (and 88 additional North of the Wall groups), however they have all banded together under Mance Rayder as a mega army to defeat the men of Castle Black.

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Character on Character Fights:

Cersei Lannister wants Tyrion to suffer for betrothing Myrcella to Trystane from House Martell of Dorne and the killing of Joffrey and for killing her Mother (in her eyes).

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Game of Thrones: Threads at the TV Critic